Timothy Geithner should tell his father-in-law to keep his voice down in restaurants — because he is publicly trumpeting that the US Treasury secretary has an agreed exit strategy from the tough job.

Food critic Albert Sonnenfeld, whose daughter, Carole, is wed to the country’s top money man, stunned strangers at Bar Boulud Thursday night when he claimed President Obama’s nomination of Dartmouth College president Dr. Jim Yong Kim to head the World Bank was part of a plan to allow Geithner to take over the Ivy League school’s top post, reports The Post’s Jeane MacIntosh.

“That’s why Obama nominated [Kim] for the World Bank — so that there’d be an opening,” Sonnenfeld claimed to a dinner companion at the eatery’s communal table.

Seated with five other couples he didn’t know, Sonnenfeld indiscreetly claimed Geithner has since changed his mind. “They offered him the presidency of Dartmouth. But now he doesn’t want it,” said the gabby granddad. “He wants something else.”

His claims came after Kim got the World Bank job ahead of Nigerian finance minister Ngozi Okonjo-Iweala, believed by some to be the more qualified candidate.

Sonnenfeld quickly turned the chat to Geithner. “My daughter is, of course, married to Tim Geithner,’ and followed with, ‘He’s stepping down at the end of the year, after the election,” recounted the diner.

Sonnenfeld also let slip that Carole Geithner “can’t wait to get out” of DC because “she has to hold her nose and entertain all these Republicans.” Sonnenfeld added, according to the witness, “Some of them she actually liked, like Jim Bunning from Kentucky. But now he’s gone. Can you imagine having to entertain John Boehner and his wife, with his fake tan?”

Geithner spokesman Anthony Coley told us, “Interesting theory about Dartmouth, but to paraphrase Kissinger: ‘It has the disadvantage of being made up. ’ ”